Sum Equals Xor

AtCoder

IDabc129_e

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $L$ in base two. How many pairs of non-negative integers $(a, b)$ satisfy the following conditions? * $a + b \leq L$ * $a + b = a \text{ XOR } b$ Since there can be extremely many such pairs, print the count modulo $10^9 + 7$. What is XOR? The XOR of integers $A$ and $B$, $A \text{ XOR } B$, is defined as follows: * When $A \text{ XOR } B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if either $A$ or $B$, but not both, has $1$ in the $2^k$'s place, and $0$ otherwise. For example, $3 \text{ XOR } 5 = 6$. (In base two: $011 \text{ XOR } 101 = 110$.) ## Constraints * $L$ is given in base two, without leading zeros. * $1 \leq L < 2^{100\ 001}$ ## Input Input is given from Standard Input in the following format: $L$ [samples]

Samples

Input #1

Output #1

5

Five pairs $(a, b)$ satisfy the conditions: $(0, 0), (0, 1), (1, 0), (0, 2)$ and $(2, 0)$.

Input #2

1111111111111111111

Output #2

162261460

API Response (JSON)

{
  "problem": {
    "name": "Sum Equals Xor",
    "description": {
      "content": "You are given a positive integer $L$ in base two. How many pairs of non-negative integers $(a, b)$ satisfy the following conditions? *   $a + b \\leq L$ *   $a + b = a \\text{ XOR } b$ Since there can",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc129_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a positive integer $L$ in base two. How many pairs of non-negative integers $(a, b)$ satisfy the following conditions?\n\n*   $a + b \\leq L$\n*   $a + b = a \\text{ XOR } b$\n\nSince there can...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments